Sequential estimate for generalized linear models with uncertain number of effective variables

For the generalized linear model, the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter. This method can determine a minimum sample size under which effective variables contributing to the model are identified and estimates of regression parameters achieve the required accuracy. The authors prove that the proposed sequential procedure is asymptotically optimal. Numerical simulation studies show that the proposed method can save a large number of samples compared to the traditional sequential approach.